1. Field of the Invention
This invention relates to flight control systems that mitigate the effects of flexible body dynamics on flight vehicles such as missiles.
2. Description of the Related Art
Missile flight control systems receive rate and acceleration measurements from an on-board Inertial Measurement Unit (IMU) and apply a flight control law to actuate control surfaces (e.g. fins) to effectuate a guidance command. The missile's airframe flexes as it translates through the air. These flexible body dynamics introduce an unwanted signal to the control loop response. The flight control system must be designed to compensate for these flexible body dynamics or the system could have self-exciting vibrations. In the case where these vibrations are not bounded, catastrophic structural damage and mission failure will occur. In the case where the vibrations remain finite, the additional frequency content in the actuator commands can lead to actuator failure due to overheating and mission failure.
The airframe 10 experiences several different types of flexible body modes under the different loads as it flies through the air including a 1st lateral bending mode 12 and a 2nd lateral bending mode 14 as shown in FIGS. 1a and 1b, respectively, along the pitch and yaw channels, a 1st torsional mode and various fin modes. The 1st lateral bending mode is the most important. In a long cylindrically shaped body such as found in a missile or comparable flight vehicle, the 1st lateral bending mode has the lowest frequency that lies within or within about a decade above the gain cross-over of the controller bandwidth. The specific amplitude and frequency depend on the missile design, the uncertainty in the manufactured components such as the actuators and the changing load conditions. If the flight controller has sufficient bandwidth and minimal latency it may be possible to actuate the control surface to directly compensate the 1st lateral bending mode but this requires a lot of power and places considerable stress on the actuators and flight controller. Other higher frequency modes including the 2nd lateral bending, torsion and fin modes have less effect on the control loop.
In the absence of these flexible body modes the open loop frequency response of a well designed control loop will have the following typical characteristics: 1) high gain at low frequency for good command tracking and disturbance rejection; 2) a slope of between 20 and 40 dB/decade as the gain crosses 0 dB (“gain crossover”) for good robustness to time delays; and 3) a slope of at least 20 dB decade above the crossover frequency to attenuate high frequency noise. The difference between the phase and −180° at the gain cross-over is referred to as the “phase margin” and is a measure of the control loop's sensitivity to unmodeled time delays. The difference between the gain and 0 dB at the frequency where the phase passes through −180° (the phase cross-over) is referred to as the “gain margin” and is a measure of the sensitivity of the control loop to gain uncertainties. These margins are normally not independent, as a change in the gain response affects the gain at the phase crossover (gain margin) as well as the frequency at which the gain crossover occurs, which is the frequency used to compute the phase margin. In general, the open-loop phase margin and gain margin should be large to ensure a robust control loop. If the phase-margin is too small then small unmodeled time delays in the real system could result in an unstable control loop. If the gain-margin is too small then small variations in the real system gain could result in an unstable control loop. In missiles and other flight vehicles, the 1st lateral bending mode is typically large enough that the gain of the control loop at the mode frequency, which would otherwise be −20 to −30 dB, is greater than 0 dB, and thus has the potential to become self-excited and destabilize the control loop. Accordingly, the flight control system must be configured to attenuate at least the 1st lateral bending modes and preferably the other higher order modes as well.
One way to compensate for the 1st lateral bending mode is to design the actuator, fins, and IMU placement so that the control loop actively dampens the mode. This is referred to as a phase-compensated control system, in which the actuators are designed to have a higher bandwidth and to actively dampen the 1st lateral bending mode. As a result, the phase is suitably 50-65 degrees (ideally 180 degrees) out-of-phase at the 1st lateral bending mode frequency so that the control loop does not reinforce the mode and cause it to self-excite. This approach can work but is expensive because the actuator mechanisms must be carefully designed and manufactured to dampen and not excite the 1st lateral bending modes and the location of the IMU is critical.
A more common approach is a gain-compensated control system in which digital filters are used to attenuate the flexible body modes. As shown in FIG. 2, a typical flight control system 20 (shown here for the pitch channel) includes a guidance system 22 that provides a guidance command AZC, typically a lateral acceleration command, an IMU 24 including accelerometers and gyros that provide measurements of the acceleration AZM and pitch rate QM, and a flight controller 26 that applies a control law to the guidance command and measured data to issue commands to actuate the control surfaces and effectuate the guidance command. Rate feedback is typically used to augment the stability of the airframe, and acceleration feedback is used to track the guidance command.
The measured rate and acceleration include a desired rigid airframe component that is needed to property control the missile and an unwanted flexible airframe component due to the various flexible body modes. To avoid further exciting the flexible airframe dynamics, a set of digital filters 28 is used to attenuate the unwanted flexible airframe component of the measured rates and accelerations so that the measurements more closely represent only the rigid airframe component. A 1st lateral bending mode digital notch filter (NF) 30 is specially designed for both the yaw and pitch measured rates and accelerations to provide gain-compensation to adequately suppress the effects of the 1st lateral bending modes. Higher frequency mode filters 32 are a suitable combination of low-pass filters (LPFs) and NFs that are designed to attenuate the measured 2nd lateral bending, torsional and fin modes and not introduce significant phase loss or latency.
As shown in FIG. 3a, a typical 1st lateral bending mode digital notch filter 30 has a gain response 50 to attenuate the measured response of the 1st lateral bending mode. A characteristic of causal digital notch filters is that they start to induce phase loss approximately a decade below the notch, and that the wider and deeper the notch the greater the phase loss. The phase response 52 associated with the gain response 50 is shown in FIG. 3b. In this case the digital notch filter introduces significant phase loss, approximately 10°, at frequencies within the flight control bandwidth (in this case <10 Hz). Phase loss is a non-dimensional measure of latency which negatively affects the flight control system's ability to track the input commands. Too much latency can result in an unstable closed loop system. If the notch filter could be designed to be very narrow and only deep enough to attenuate the mode sufficiently, the amount of latency may be acceptable. However, this is impractical due to the inherent uncertainty of the flexible dynamics that results from the variability that occurs during the missile manufacture. Furthermore, the mode frequency and shape change as fuel is consumed, or as the missile stages are dropped. Additionally the amount of attenuation needed varies with flight condition (Mach number and altitude). Often, the digital notch filters are designed to shift with the frequency, and vary with flight condition, but manufacturing uncertainty necessitates wider and deeper notch filters. As digital notch filters are inexpensive to implement and well understood, they are an adequate solution for those applications that can tolerate the bandwidth limitations they place on the flight control system.
As shown in FIGS. 4a-4b and 5a-5b, the magnitude 53 of the frequency response exhibits a gain margin 54 of approximately 3.4 dB and the phase 55 exhibits a phase margin 56 of approximately 16.9°. Furthermore, the gain response at the 1st lateral bending mode frequency peaks up to about −10 dB even with the digital notch filter. In many systems this would be considered either marginally acceptable or unacceptable because both the gain margin and phase margin are lower than would typically be allowed (4 dB and 20° being typical gain and phase margin design goals).
Another approach is to carefully position multiple IMUs about the airframe and process the data to cancel out the effects of the lower frequency flexible body dynamics. This approach has been used in very large expensive rockets whose lower frequency flexible body mode frequencies are within the bandwidth of the flight control system required to stabilize the rocket. These rockets can afford both the cost, additional space, and additional weight associated with multiple IMUs. This approach is not practical for small low cost lightweight missiles whose lower frequency flexible body mode frequencies are at least ½ a decade to a decade above the bandwidth of the flight control system.
Customers are demanding lighter cheaper missiles and higher performance in both speed and maneuverability. These requirements are directly at odds. Lighter cheaper and consequently more compliant airframes experience larger amplitude flexible body dynamics at lower frequencies than a more expensive stiffer airframe, particularly the 1st lateral bending mode which limits the flight control bandwidth and therefore the speed of response. Current solutions are too expensive, bulky and heavy, or cause too much latency so that they fail the maneuverability specification.